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We analyze a two species discrete predator-prey model in which the prey disperses between two patches of a heterogeneous environment with barriers and the mature predator disperses between the patches with no barrier. By using the discrete dynamical system generated by a monotone, concave maps for subcommunity of prey, we obtain the subcommunity of prey exists an equilibrium which attracts all positive solutions, and using the stability trichotomy results on the monotone and continuous operator, we obtain some sufficient conditions for the permanence of species. These results are applied to the models with rational growth functions and exponential growth functions. We also present numerical examples to illustrate the dynamic complexity of systems.

@article{Tang2001, abstract = {We analyze a two species discrete predator-prey model in which the prey disperses between two patches of a heterogeneous environment with barriers and the mature predator disperses between the patches with no barrier. By using the discrete dynamical system generated by a monotone, concave maps for subcommunity of prey, we obtain the subcommunity of prey exists an equilibrium which attracts all positive solutions, and using the stability trichotomy results on the monotone and continuous operator, we obtain some sufficient conditions for the permanence of species. These results are applied to the models with rational growth functions and exponential growth functions. We also present numerical examples to illustrate the dynamic complexity of systems.}, author = {Tang, Sanyi, Chen, Lansun}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique}, keywords = {age-structure; natural barrier; subcommunity; persistence; discrete predator-prey model; discrete dynamic system; stability trichotomy}, language = {eng}, number = {4}, pages = {675-690}, publisher = {EDP-Sciences}, title = {A discrete predator-prey system with age-structure for predator and natural barriers for prey}, url = {http://eudml.org/doc/194068}, volume = {35}, year = {2001},}

TY - JOURAU - Tang, SanyiAU - Chen, LansunTI - A discrete predator-prey system with age-structure for predator and natural barriers for preyJO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse NumériquePY - 2001PB - EDP-SciencesVL - 35IS - 4SP - 675EP - 690AB - We analyze a two species discrete predator-prey model in which the prey disperses between two patches of a heterogeneous environment with barriers and the mature predator disperses between the patches with no barrier. By using the discrete dynamical system generated by a monotone, concave maps for subcommunity of prey, we obtain the subcommunity of prey exists an equilibrium which attracts all positive solutions, and using the stability trichotomy results on the monotone and continuous operator, we obtain some sufficient conditions for the permanence of species. These results are applied to the models with rational growth functions and exponential growth functions. We also present numerical examples to illustrate the dynamic complexity of systems.LA - engKW - age-structure; natural barrier; subcommunity; persistence; discrete predator-prey model; discrete dynamic system; stability trichotomyUR - http://eudml.org/doc/194068ER -

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